Proceedings of the Japan Academy, Series A, Mathematical Sciences

Non-left-orderable surgeries on negatively twisted torus knots

Kazuhiro Ichihara and Yuki Temma

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We show that certain negatively twisted torus knots admit Dehn surgeries yielding 3-manifolds with non-left-orderable fundamental groups.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 5 (2018), 49-52.

First available in Project Euclid: 27 April 2018

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Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Dehn surgery left-orderable group twisted torus knots


Ichihara, Kazuhiro; Temma, Yuki. Non-left-orderable surgeries on negatively twisted torus knots. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 5, 49--52. doi:10.3792/pjaa.94.49.

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  • S. Boyer, C. McA. Gordon and L. Watson, On L-spaces and left-orderable fundamental groups, Math. Ann. 356 (2013), no. 4, 1213–1245.
  • K. Christianson, J. Goluboff, L. Hamann and S. Varadaraj, Non-left-orderable surgeries on twisted torus knots, Proc. Amer. Math. Soc. 144 (2016), no. 6, 2683–2696.
  • A. Clay and L. Watson, Left-orderable fundamental groups and Dehn surgery, Int. Math. Res. Not. IMRN 2013, no. 12, 2862–2890.
  • J. C. Dean, Small Seifert-fibered Dehn surgery on hyperbolic knots, Algebr. Geom. Topol. 3 (2003), 435–472.
  • K. Ichihara and Y. Temma, Non-left-orderable surgeries and generalized Baumslag-Solitar relators, J. Knot Theory Ramifications 24 (2015), no. 1, 1550003, 8 pp.
  • Y. Nakae, A good presentation of $(-2,3,2s+1)$-type pretzel knot group and $\mathbf{R}$-covered foliation, J. Knot Theory Ramifications 22 (2013), no. 1, 1250143, 23 pp.
  • P. S. Ozsváth and Z. Szabó, Knot Floer homology and rational surgeries, Algebr. Geom. Topol. 11 (2011), no. 1, 1–68.
  • F. Vafaee, On the knot Floer homology of twisted torus knots, Int. Math. Res. Not. IMRN 2015, no. 15, 6516–6537.